We report on a scanning tunnelling microscopy (STM) study, with different C-60, thin-film growth orientations, on As-rich 2 X 6 and 2 x 4 surfaces of GaAs(001) prepared by molecular beam epitaxy. On the 2 X 6 As surface, the corrugated potential of the 2 x 6 substrate forces the first monolayer to be strongly modified, resulting in the formation of a ’double-chain’ commensurate structure. C-60-substrate interaction, however, is limited to 2 or 3 monolayers from the interface and a competing intermolecular interaction governs the 3-dimensional growth of multiple-layer C-60 FCC crystalline film. Even though both surfaces have similar strongly corrugated potentials, an unusual (110)-oriented C-60 thin crystalline film grows on the 2 X 4 beta phase. This novel growth can be understood in terms of a site-specific interaction between the substrate and the molecule and the interplay of the competing intermolecular interactions.